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A174640 A triangular sequence:t(n,m)=A033306(n,m)-A033306(n,0)+1.

%I A174640 #5 Jun 02 2025 02:44:38
%S A174640 1,1,1,1,1,1,1,2,2,1,1,6,10,6,1,1,24,49,49,24,1,1,110,248,298,248,110,
%T A174640 1,1,545,1308,1749,1749,1308,545,1,1,2877,7229,10421,11611,10421,7229,
%U A174640 2877,1,1,16114,41998,64114,77134,77134,64114,41998,16114,1,1,95496
%N A174640 A triangular sequence:t(n,m)=A033306(n,m)-A033306(n,0)+1.
%C A174640 Row sums are:
%C A174640 1, 2, 3, 6, 24, 148, 1016, 7206, 52667, 398722, 3137084,...
%D A174640 This notebook downloaded from https://mathworld.wolfram.com/notebooks/Combinatorics/BellNumber.nb.
%D A174640 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 80.
%F A174640 t(n,m)=A033306(n,m)-A033306(n,0)+1
%e A174640 {1},
%e A174640 {1, 1},
%e A174640 {1, 1, 1},
%e A174640 {1, 2, 2, 1},
%e A174640 {1, 6, 10, 6, 1},
%e A174640 {1, 24, 49, 49, 24, 1},
%e A174640 {1, 110, 248, 298, 248, 110, 1},
%e A174640 {1, 545, 1308, 1749, 1749, 1308, 545, 1},
%e A174640 {1, 2877, 7229, 10421, 11611, 10421, 7229, 2877, 1},
%e A174640 {1, 16114, 41998, 64114, 77134, 77134, 64114, 41998, 16114, 1},
%e A174640 {1, 95496, 256626, 410226, 523476, 565434, 523476, 410226, 256626, 95496, 1}
%t A174640 b[0] := 1;
%t A174640 b[n_] := b[n] = Total[Table[b[k]Binomial[n - 1, k], {k, 0, n - 1}]];
%t A174640 a = b /@ Range[0, 70];
%t A174640 t[n_, m_] := Binomial[n, m]*a[[m + 1]]*a[[n - m + 1]];
%t A174640 Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
%t A174640 Flatten[%]
%Y A174640 A033306
%K A174640 nonn,tabl,uned
%O A174640 0,8
%A A174640 _Roger L. Bagula_, Mar 25 2010